During the past nine years our group has investigated various forms of k-space and temporal undersampling relative to the Nyquist Theorem for faster acquisitions in challenging MR imaging applications, particularly time resolved, high resolution contrast-enhanced angiography. Using 3D TRICKS, a temporal undersampling factor of 3 was achieved to provide time resolved 3D MR angiograms. Later, in-plane radially undersampled acquisitions were developed for acquiring angiograms with angular undersampling factors of 6. The combination of these two techniques in PR TRICKS resulted in undersampling factors of 18. Undersampling was extended to a truly 3D radial trajectory with VIPR, where typical undersampling factors of 50 can be used without significant artifacts in certain applications. In addition, VIPR has been combined with phase contrast imaging to permit 3D flow measurements across a large volume enabling the derivation of pressure gradients in small vessels. [unreadable] Recently, we developed the concept for an approximate non-iterative reconstruction technique called HYPR (HighlY constrained back PRojection) to further increase the permissible undersampling of temporally evolving acquisitions by another large factor that depends on the sparsity of the data set and the degree of spatio- temporal correlation between the serial images. Preliminary results have produced undersampling factors between 100 and 300 for contrast-enhanced angiography. A factor of nearly 1000 was achieved with adequate SNR in a 4 minute 3843 time-resolved phase contrast examination that would have required 39 hours using conventional Cartesian phase encoding methods. The technique was also used to achieve a factor of ten dose reduction in X-ray CT perfusion and can be generalized to other image series applications such as MR diffusion tensor imaging where the technique has simulated a factor of 15 undersampling in a 2D implementation using a series of images having different diffusion encoding directions. A large number of other potential applications that are not proposed here will benefit from a better understanding of the proposed algorithm and its potential limitations. [unreadable] HYPR provides unique SNR behavior by transferring the SNR obtained in a long composite image into individual time frames. The duration of this composite image must be adjusted for each clinical application so that spatial blurring and waveform distortion can be minimized. This depends on sparsity and spatio-temporal correlation conditions. [unreadable] We propose to investigate the basic properties of HYPR using computer simulations and phantoms and to conduct three preliminary patient studies to establish protocols to be used in future validation studies. This proposal focuses on the evaluation of cerebral AVMs using PR HYPR TRICKS and HYPR VIPR and the measurement of pressure gradients across stenotic carotid arteries. [unreadable] [unreadable] [unreadable]